Question 908637: Evaluate the following limits by using the L'Hopital's Theorem
a. lim as x approaches to positive infinity (2^x)/(e^(x^2)) Found 2 solutions by rothauserc, solver91311:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! a) f(x) = 2^x and g(x) = e^(x^2)
f'(x) = 2^x * log(2)
g'(x) = 2e^(x^2)x
then lim as x approaches infinity is 2^x * log(2) / (2e^(x^2)x = L
we see that lim as x approaches infinity of g(x) is +infinity which satisfies L'Hopital's Theorem criteria and
lim as x approaches infinity is 2^x * log(2) / (2e^(x^2)x = 1
b) lim as x approaches to 0 (sinx)^lncosx is 1
The problem cannot be solved using L'Hopital because every derivative of contains a factor of and therefore increases without bound as increases without bound. Likewise, every derivative of contains a factor of and therefore increases without bound as increases without bound.
John
My calculator said it, I believe it, that settles it
